Changing numbers on a cube so that they're all equal
Source: 2011 Czech & Slovak MO, District Round, Category A
August 13, 2011
geometry3D geometrycombinatorics unsolvedcombinatorics
Problem Statement
Let be a set of six distinct positive integers whose sum is . These numbers are written on the faces of a cube, one number to each face. A move consists of choosing three faces of the cube that share a common vertex and adding to the numbers on those faces. Determine the number of sets for which it’s possible, after a finite number of moves, to produce a cube all of whose sides have the same number.